Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use Pascal's Triangle to complete the expansion of $(w + x)^6$ . $\newline$ $w^6 + 6w^5x + \_\_\_\_w^4x^2 + 20w^3x^3 + 15w^2x^4 + 6wx^5 + x^6$

View step-by-step help

View step-by-step help

Pascal's triangle and the Binomial Theorem

Full solution

Q. Use Pascal's Triangle to complete the expansion of

(w + x)^6

.

\newline

w^6 + 6w^5x + \_\_\_\_w^4x^2 + 20w^3x^3 + 15w^2x^4 + 6wx^5 + x^6

Look at Pascal's Triangle: Look at Pascal's Triangle to find the coefficients for the expansion of $(w + x)^6$ . The $7$ th row (since we start counting from $0$ ) is $1, 6, 15, 20, 15, 6, 1$ .
Identify coefficients needed: We already have the coefficients for $w^6$ , $w^5x$ , $w^3x^3$ , $w^2x^4$ , $wx^5$ , and $x^6$ . We need the coefficient for $w^4x^2$ .
Calculate coefficient for $w^4x^2$ : The coefficient for $w^4x^2$ is the $4$ th number in the $7$ th row of Pascal's Triangle, which is $15$ .

More problems from Pascal's triangle and the Binomial Theorem

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 2 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 1 month ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 2 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 2 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 2 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 2 months ago